Abstract
Artificial Immune Systems (AIS) are an emerging new field of research in Computational Intelligence that are applied to many areas of application, e.g., optimization, anomaly detection and classification. For optimization tasks, the use of hypermutation operators constitutes a common concept in AIS. By now, only little theoretical work has been done in this field. In this paper, we present a detailed theoretical runtime analysis that gives an insight into the dynamics of fitness based hypermutation processes. Two specific mutation rates are considered using a simple immune inspired algorithm. Our main focus lies thereby on the influence of parameters embedded in popular immune inspired hypermutation operators from the literature. Our theoretical findings are accompanied by some empirical results.
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References
Dasgupta, D. (ed.): Artificial Immune Systems and Their Applications. Springer, Heidelberg (1998)
de Castro, L.N., Timmis, J.: Artificial Immune Systems: A New Computational Intelligence Approach. Springer, Heidelberg (2002)
Timmis, J., Andrews, P.S., Owens, N., Clark, E.: An interdisciplinary perspective on artificial immune systems. Evolutionary Intelligence 1, 5–26 (2008)
Burnet, F.M.: The Clonal Selection Theory of Acquired Immunity. Cambridge University Press, Cambridge (1959)
de Castro, L.N., Zuben, F.J.V.: Learning and Optimization Using the Clonal Selection Principle. IEEE Trans. on Evol. Comp. 6(3), 239–251 (2002)
Cutello, V., Nicosia, G., Pavone, M.: Exploring the Capability of Immune Algorithms: A Characterization of Hypermutation Operators. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 263–276. Springer, Heidelberg (2004)
Kelsey, J., Timmis, J.: Immune Inspired Somatic Contiguous Hypermutation for Function Optimisation. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 207–218. Springer, Heidelberg (2003)
Cortés, N.C., Coello, C.A.C.: Multiobjective Optimization Using Ideas from the Clonal Selection Principle. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 158–170. Springer, Heidelberg (2003)
Timmis, J.: Artificial Immune Systems – Today and Tomorrow. Natural Computing 6(1), 1–18 (2007)
Hart, E., Timmis, J.: Application Areas of AIS: The Past, the Present and the Future. Applied Soft Computing 8(1), 191–201 (2008)
Timmis, J., Hone, A., Stibor, T., Clark, E.: Theoretical Advances in Artificial Immune Systems. Theoretical Computer Science (in press, 2008)
Villalobos-Arias, M., Coello Coello, C.A., Hernández-Lerma, O.: Convergence analysis of a multiobjective artificial immune system algorithm. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 226–235. Springer, Heidelberg (2004)
Clark, E., Hone, A., Timmis, J.: A Markov Chain Model of the B-Cell Algorithm. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 318–330. Springer, Heidelberg (2005)
Cutello, V., Nicosia, G., Romeo, M., Oliveto, P.S.: On the Convergence of Immune Algorithms. In: Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (FOCI 2007), pp. 409–415. IEEE Press, Los Alamitos (2007)
Jansen, T., Wegener, I.: On the Choice of the Mutation Probability for the (1+1) EA. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 89–98. Springer, Heidelberg (2000)
Jansen, T., Sudholt, D.: Design and analysis of an asymmetric mutation operator. In: Proceedings of the 2005 IEEE Congress on Evolutionary Computation (CEC 2005). IEEE Press, Los Alamitos (2005)
Doerr, B., Hebbinghaus, N., Neumann, F.: Speeding Up Evolutionary Algorithms through Asymmetric Mutation Operators. Evol. Comput. 15(4), 401–410 (2007)
Schwefel, H.-P.: Evolution and Optimum Seeking. Wiley & Sons, Chichester (1995)
Droste, S., Jansen, T., Wegener, I.: On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science 276(1-2), 51–81 (2002)
Hagerup, T., Rüb, C.: A guided tour of Chernoff bounds. Information Processing Letters 33, 305–308 (1990)
de Castro, L.N., Timmis, J.: An Artificial Immune Network for Multimodal Function Optimization. In: Proceedings of the 2002 IEEE Congress on Evolutionary Computation (CEC 2002), pp. 674–699. IEEE Press, Los Alamitos (2002)
Cutello, V., Narzisi, G., Nicosia, G., Pavone, M.: Clonal selection Algorithms: A Comparative Case Study Using Effective Mutation Potentials. In: Jacob, C., Pilat, M.L., Bentley, P.J., Timmis, J. (eds.) ICARIS 2005. LNCS, vol. 3627, pp. 13–28. Springer, Heidelberg (2005)
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Zarges, C. (2008). Rigorous Runtime Analysis of Inversely Fitness Proportional Mutation Rates. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87700-4_12
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DOI: https://doi.org/10.1007/978-3-540-87700-4_12
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